Difference between revisions of "Cascaded Bandpass Filter"
Line 2: | Line 2: | ||
== Analysis == | == Analysis == | ||
+ | The cascaded bandpass filter uses a first-order lowpass filter, followed by a first-order highpass filter, followed by an inverting amplifier to raise or lower to total passband gain to some desired level. The equation given is: | ||
+ | <center><math> | ||
+ | \begin{align} | ||
+ | H&=\frac{V_o}{V_i}= | ||
+ | \left(-\frac{1}{1+j\omega C_1R} \right) | ||
+ | \left(-\frac{j\omega C_2R}{1+j\omega C_2R} \right) | ||
+ | \left(-\frac{R_f}{R_i}\right) | ||
+ | \end{align} | ||
+ | \</center></math> | ||
+ | |||
Revision as of 20:43, 22 March 2010
This page analyzes a cascaded bandpass filter - specifically the one proposed in Alexander & Sadiku Fig. 14.45.
Analysis
The cascaded bandpass filter uses a first-order lowpass filter, followed by a first-order highpass filter, followed by an inverting amplifier to raise or lower to total passband gain to some desired level. The equation given is:
Without inductors, the most likely candidate for such a filter would be the filter on p. 439 of the Rizzoni text[1] which uses a series combination of a resistor and capacitor as \(Z_N\) and a parallel combination as \(Z_F\). This leads to an overall transfer function of:
or, as re-cast in class,
To make life a little easier, let's call
which means
This means the bandwidth and natural frequency squared are, respectively,
- ↑ Rizzoni, Giorgio. Principles and applications of electrical engineering / Giorgio Rizzoni, Tom Hartley. - 5th ed. McGraw-Hill, 2007.